Store stable for how long? In theory no element is perfectly and infinitely stable. Quantum effects preclude it. (Hydrogen nucleus maybeee excepting, depends on the half-life of the proton when they figure it out).
So I'd be looking at transmuting not storing. Preferably very common universally, and very dense indeed, and use that as raw material to to make other stuff on demand or to replenish needed stocks to the right level.
Hydrogen is one obvious universal candidate for a raw material - and I think future hand waving allows us to project a means of storing it in its very dense metallic form (also helpful for its useful heat/conduction effects as well as density, and energy density too). Alternatively, if you can handle compact matter, a few teaspoons of that (think neutron star material either from a star or human-made) will give you supplies for ages.
Containment and control would be tricky but probably solved for either of these by the time you can get these in useful quantities. For example, maybe stability is possible at a temperature or pressure we can realistically achieve, or specific forms or methods mean these are less of an issue. After all we dont know much right now except that they exist, but terms like "compact matter" cover many many kinds of physical entity, some more stable or amenable than others perhaps. when we get closer to them. That's about how room temperature superconductor research is progressing, and just when you thought that was an absolute limit, it turns out it wasnt. Even if we dont know an exact solution right now, hand waving the containment issue away or just about manageable or solved by that time, seems fair.
Your next need is a way to transmute these to useful basic building blocks. I think if we grant a technology that can store and manipulate these, it can also probably make from them a wide range of useful basic elements, molecules and simple compounds without much effort.
This actually isn't "too" far ahead technologically. We've had tentative reports we might have briefly created metallic hydrogen in the lab, laser fusion research has created exceedingly high densities fleetingly, the LHC has reported quark-gluon plasma, so perhaps compact matter should be feasible to create or obtain in the order of several decades to a couple of centuries, and by then turning these into most other elements, or elements into basic molecules won't be far behind.
At that point you need a means of manufacturing prototype objects from schematics (that's your complex devices, protein molecules, tasty food etc) and from these. Think 3d printing a couple of centuries time. Should be reasonable even for extremely complex molecules, food, device parts, even on a large scale (scaling up is what industry does all the time with discoveries, so I imagine a way will be found!)
Which brings us to the last requirement: Your biggest need then is likely to be energy. Lots of it. This stuff will not be cheap in energy terms. That's the last ingredient. Fortunately dense hydrogen (and indeed many other universally available things) are able to sort that out for you -again in a few decades to a couple of centuries.
Last problem is... People! Will they get bored!